AI Image Generators

Explore the best AI Image Generators — independent reviews, comparisons, pricing and step-by-step how-to guides, curated by Aizhi.

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  Distribution management system

  A distribution management system (DMS) is a collection of applications designed to monitor and control the electric power distribution networks efficiently and reliably. It acts as a decision support system to assist the control room and field operating personnel with the monitoring and control of the electric distribution system. Improving the reliability and quality of service in terms of reducing power outages, minimizing outage time, maintaining acceptable frequency and voltage levels are the key deliverables of a DMS. Given the complexity of distribution grids, such systems may involve communication and coordination across multiple components. For example, the control of active loads may require a complex chain of communication through different components as described in US patent 11747849B2 In recent years, utilization of electrical energy increased exponentially and customer requirement and quality definitions of power were changed enormously. As electric energy became an essential part of daily life, its optimal usage and reliability became important. Real-time network view and dynamic decisions have become instrumental for optimizing resources and managing demands, leading to the need for distribution management systems in large-scale electrical networks. == Overview == Most distribution utilities have been comprehensively using IT solutions through their Outage Management System (OMS) that makes use of other systems like Customer Information System (CIS), Geographical Information System (GIS) and Interactive Voice Response System (IVRS). An outage management system has a network component/connectivity model of the distribution system. By combining the locations of outage calls from customers with knowledge of the locations of the protection devices (such as circuit breakers) on the network, a rule engine is used to predict the locations of outages. Based on this, restoration activities are charted out and the crew is dispatched for the same. In parallel with this, distribution utilities began to roll out Supervisory Control and Data Acquisition (SCADA) systems, initially only at their higher voltage substations. Over time, use of SCADA has progressively extended downwards to sites at lower voltage levels. DMSs access real-time data and provide all information on a single console at the control centre in an integrated manner. Their development varied across different geographic territories. In the US, for example, DMSs typically grew by taking Outage Management Systems to the next level, automating the complete sequences and providing an end to end, integrated view of the entire distribution spectrum. In the UK, by contrast, the much denser and more meshed network topologies, combined with stronger Health & Safety regulation, had led to early centralisation of high-voltage switching operations, initially using paper records and schematic diagrams printed onto large wallboards which were 'dressed' with magnetic symbols to show the current running states. There, DMSs grew initially from SCADA systems as these were expanded to allow these centralised control and safety management procedures to be managed electronically. These DMSs required even more detailed component/connectivity models and schematics than those needed by early OMSs as every possible isolation and earthing point on the networks had to be included. In territories such as the UK, therefore, the network component/connectivity models were usually developed in the DMS first, whereas in the USA these were generally built in the GIS. The typical data flow in a DMS has the SCADA system, the Information Storage & Retrieval (ISR) system, Communication (COM) Servers, Front-End Processors (FEPs) & Field Remote Terminal Units (FRTUs). == Why DMS? == Reduce the duration of outages Improve the speed and accuracy of outage predictions. Reduce crew patrol and drive times through improved outage locating. Improve the operational efficiency Determine the crew resources necessary to achieve restoration objectives. Effectively utilize resources between operating regions. Determine when best to schedule mutual aid crews. Increased customer satisfaction A DMS incorporates IVR and other mobile technologies, through which there is an improved outage communications for customer calls. Provide customers with more accurate estimated restoration times. Improve service reliability by tracking all customers affected by an outage, determining electrical configurations of every device on every feeder, and compiling details about each restoration process. == DMS Functions == In order to support proper decision making and O&M activities, DMS solutions should support the following functions: Network visualization & support tools Applications for Analytical & Remedial Action Utility Planning Tools System Protection Schemes The various sub functions of the same, carried out by the DMS are listed below:- === Network Connectivity Analysis (NCA) === Distribution network usually covers over a large area and catering power to different customers at different voltage levels. So locating required sources and loads on a larger GIS/Operator interface is often very difficult. Panning & zooming provided with normal SCADA system GUI does not cover the exact operational requirement. Network connectivity analysis is an operator specific functionality which helps the operator to identify or locate the preferred network or component very easily. NCA does the required analyses and provides display of the feed point of various network loads. Based on the status of all the switching devices such as circuit breaker (CB), Ring Main Unit (RMU) and/or isolators that affect the topology of the network modeled, the prevailing network topology is determined. The NCA further assists the operator to know operating state of the distribution network indicating radial mode, loops and parallels in the network. === Switching Schedule & Safety Management === In territories such as the UK a core function of a DMS has always been to support safe switching and work on the networks. Control engineers prepare switching schedules to isolate and make safe a section of network before work is carried out, and the DMS validates these schedules using its network model. Switching schedules can combine telecontrolled and manual (on-site) switching operations. When the required section has been made safe, the DMS allows a Permit To Work (PTW) document to be issued. After its cancellation when the work has been finished, the switching schedule then facilitates restoration of the normal running arrangements. Switching components can also be tagged to reflect any Operational Restrictions that are in force. The network component/connectivity model, and associated diagrams, must always be kept absolutely up to date. The switching schedule facility therefore also allows 'patches' to the network model to be applied to the live version at the appropriate stage(s) of the jobs. The term 'patch' is derived from the method previously used to maintain the wallboard diagrams. === State Estimation (SE) === The state estimator is an integral part of the overall monitoring and control systems for transmission networks. It is mainly aimed at providing a reliable estimate of the system voltages. This information from the state estimator flows to control centers and database servers across the network. The variables of interest are indicative of parameters like margins to operating limits, health of equipment and required operator action. State estimators allow the calculation of these variables of interest with high confidence despite the facts that the measurements may be corrupted by noise, or could be missing or inaccurate. Even though we may not be able to directly observe the state, it can be inferred from a scan of measurements which are assumed to be synchronized. The algorithms need to allow for the fact that presence of noise might skew the measurements. In a typical power system, the State is quasi-static. The time constants are sufficiently fast so that system dynamics decay away quickly (with respect to measurement frequency). The system appears to be progressing through a sequence of static states that are driven by various parameters like changes in load profile. The inputs of the state estimator can be given to various applications like Load Flow Analysis, Contingency Analysis, and other applications. === Load Flow Applications (LFA) === Load flow study is an important tool involving numerical analysis applied to a power system. The load flow study usually uses simplified notations like a single-line diagram and focuses on various forms of AC power rather than voltage and current. It analyzes the power systems in normal steady-state operation. The goal of a power flow study is to obtain complete voltage angle and magnitude information for each bus in a power system for specified load and generator real power and voltage conditions. Once this

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  Single customer view

  A single customer view is an aggregated, consistent and holistic representation of the data held by an organisation about its customers that can be viewed in one place, such as a single page. The advantage to an organisation of attaining this unified view comes from the ability it gives to analyse past behaviour in order to better target and personalise future customer interactions. A single customer view is also considered especially relevant where organisations engage with customers through multichannel marketing, since customers expect those interactions to reflect a consistent understanding of their history and preferences. However, some commentators have challenged the idea that a single view of customers across an entire organisation is either natural or meaningful, proposing that the priority should instead be consistency between the multiple views that arise in different contexts. Where representations of a customer are held in more than one data set, achieving a single customer view can be difficult: firstly because customer identity must be traceable between the records held in those systems, and secondly because anomalies or discrepancies in the customer data must be data cleansed for data quality. As such, the acquisition by an organisation of a single customer view is one potential outcome of successful master data management. Since 31 December, 2010, maintaining a single customer view, and submitting it within 72 hours, has become mandatory for financial institutions in the United Kingdom due to new rules introduced by the Financial Services Compensation Scheme.

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  Algorithm engineering

  Algorithm engineering focuses on the design, analysis, implementation, optimization, profiling and experimental evaluation of computer algorithms, bridging the gap between algorithmics theory and practical applications of algorithms in software engineering. It is a general methodology for algorithmic research. == Origins == In 1995, a report from an NSF-sponsored workshop "with the purpose of assessing the current goals and directions of the Theory of Computing (TOC) community" identified the slow speed of adoption of theoretical insights by practitioners as an important issue and suggested measures to reduce the uncertainty by practitioners whether a certain theoretical breakthrough will translate into practical gains in their field of work, and tackle the lack of ready-to-use algorithm libraries, which provide stable, bug-free and well-tested implementations for algorithmic problems and expose an easy-to-use interface for library consumers. But also, promising algorithmic approaches have been neglected due to difficulties in mathematical analysis. The term "algorithm engineering" was first used with specificity in 1997, with the first Workshop on Algorithm Engineering (WAE97), organized by Giuseppe F. Italiano. == Difference from algorithm theory == Algorithm engineering does not intend to replace or compete with algorithm theory, but tries to enrich, refine and reinforce its formal approaches with experimental algorithmics (also called empirical algorithmics). This way it can provide new insights into the efficiency and performance of algorithms in cases where the algorithm at hand is less amenable to algorithm theoretic analysis, formal analysis pessimistically suggests bounds which are unlikely to appear on inputs of practical interest, the algorithm relies on the intricacies of modern hardware architectures like data locality, branch prediction, instruction stalls, instruction latencies which the machine model used in Algorithm Theory is unable to capture in the required detail, the crossover between competing algorithms with different constant costs and asymptotic behaviors needs to be determined. == Methodology == Some researchers describe algorithm engineering's methodology as a cycle consisting of algorithm design, analysis, implementation and experimental evaluation, joined by further aspects like machine models or realistic inputs. They argue that equating algorithm engineering with experimental algorithmics is too limited, because viewing design and analysis, implementation and experimentation as separate activities ignores the crucial feedback loop between those elements of algorithm engineering. === Realistic models and real inputs === While specific applications are outside the methodology of algorithm engineering, they play an important role in shaping realistic models of the problem and the underlying machine, and supply real inputs and other design parameters for experiments. === Design === Compared to algorithm theory, which usually focuses on the asymptotic behavior of algorithms, algorithm engineers need to keep further requirements in mind: Simplicity of the algorithm, implementability in programming languages on real hardware, and allowing code reuse. Additionally, constant factors of algorithms have such a considerable impact on real-world inputs that sometimes an algorithm with worse asymptotic behavior performs better in practice due to lower constant factors. === Analysis === Some problems can be solved with heuristics and randomized algorithms in a simpler and more efficient fashion than with deterministic algorithms. Unfortunately, this makes even simple randomized algorithms difficult to analyze because there are subtle dependencies to be taken into account. === Implementation === Huge semantic gaps between theoretical insights, formulated algorithms, programming languages and hardware pose a challenge to efficient implementations of even simple algorithms, because small implementation details can have rippling effects on execution behavior. The only reliable way to compare several implementations of an algorithm is to spend an considerable amount of time on tuning and profiling, running those algorithms on multiple architectures, and looking at the generated machine code. === Experiments === See: Experimental algorithmics === Application engineering === Implementations of algorithms used for experiments differ in significant ways from code usable in applications. While the former prioritizes fast prototyping, performance and instrumentation for measurements during experiments, the latter requires thorough testing, maintainability, simplicity, and tuning for particular classes of inputs. === Algorithm libraries === Stable, well-tested algorithm libraries like LEDA play an important role in technology transfer by speeding up the adoption of new algorithms in applications. Such libraries reduce the required investment and risk for practitioners, because it removes the burden of understanding and implementing the results of academic research. == Conferences == Two main conferences on Algorithm Engineering are organized annually, namely: Symposium on Experimental Algorithms (SEA), established in 1997 (formerly known as WEA). SIAM Meeting on Algorithm Engineering and Experiments (ALENEX), established in 1999. The 1997 Workshop on Algorithm Engineering (WAE'97) was held in Venice (Italy) on September 11–13, 1997. The Third International Workshop on Algorithm Engineering (WAE'99) was held in London, UK in July 1999. The first Workshop on Algorithm Engineering and Experimentation (ALENEX99) was held in Baltimore, Maryland on January 15–16, 1999. It was sponsored by DIMACS, the Center for Discrete Mathematics and Theoretical Computer Science (at Rutgers University), with additional support from SIGACT, the ACM Special Interest Group on Algorithms and Computation Theory, and SIAM, the Society for Industrial and Applied Mathematics.

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  Informationist

  An informationist (or information specialist in context) provides research and knowledge management services in the context of clinical care or biomedical research. Although there is no one educational pathway or formalized set of skills or knowledge for informationists, one way to think of the informationist is as one who possesses the knowledge and skill of a medical librarian with extensive research specialization and some formal clinical or public health education that goes beyond on-the-job osmosis. Medical librarians and other biomedical professional organizations have been exploring the possibilities for evaluating how informationists are being used and whether their activities supplement or replace medical library activity. More generally, an informationist is a professional who works with information within a particular business, analytic or scientific context to drive toward outcomes based on evidence, analysis, prediction and execution. For example, an extension of the term is increasingly emerging in financial services, life sciences and health care industries. Though still nascently in use, its adoption applies to individuals with extensive industry expertise, acute familiarity with organizational structures and processes, deep domain level information mastery and information systems technical savvy. Informationists in this context support transformational initiatives within and across functional areas of an enterprise as architects, governance experts, continuous improvement advocates and strategists. == Background == The term was proposed in 2000 by Davidoff & Florance. Their editorial suggested that physicians should be delegating their information needs to informationists, just as they currently order CT scans from radiologists or cardiac catheterizations from cardiologists. They conceived of an information professional who was embedded in (and indeed, supported by) the clinical departments. Supporters of the concept see it as a means for librarians to reinvigorate connections with the faculty/clinicians, as well as provide superior service by dint of informationists' biomedical training. Critics complained that the idea is nothing new; librarians already provide in-depth, high quality information services and clinical medical librarians have been working alongside physicians, nurses and other clinicians for years. Large informationist programs in the U.S. exist at the National Institutes of Health and at Vanderbilt University. Welch Medical Library at Johns Hopkins University (JHU) is developing an informationist service model in which its 10 clinical and public health librarians are moving from serving as liaison librarians for assigned departments toward becoming embedded informationists within their departments. To prepare for the embedded informationist role, librarians are undertaking education as needed to supplement their backgrounds. For example, librarians bring experience in clinical behavior counseling, public health, nursing, and more. Informationist training can then focus upon filling gaps in research methods knowledge more so than on gaining additional knowledge in the librarian's area of expertise. Courses, seminars and workshops being undertaken include those covering systematic reviews, evidence-based medicine, critical appraisal, medical language, anatomy and physiology, biostatistics, and clinical research. The term informationist is related to that of informatician—also informaticist—and many informationists do possess skills in clinical topics, bioinformatics, and biomedical informatics. Harvard University, the University of Pittsburgh, and Washington University in St. Louis are examples of institutional libraries which have hired PhD-level scientists (who may or may not have library degrees) to provide informatics support for biomedical research.

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  Standard test image

  A standard test image is a digital image file used across different institutions to test image processing and image compression algorithms. By using the same standard test images, different labs are able to compare results, both visually and quantitatively. The images are in many cases chosen to represent natural or typical images that a class of processing techniques would need to deal with. Other test images are chosen because they present a range of challenges to image reconstruction algorithms, such as the reproduction of fine detail and textures, sharp transitions and edges, and uniform regions. == Historical origins == Test images as transmission system calibration material probably date back to the original Paris to Lyon pantelegraph link. Analogue fax equipment (and photographic equipment for the printing trade) were the largest user groups of the standardized image for calibration technology until the coming of television and digital image transmission systems. == Common test image resolutions == The standard resolution of the images is usually 512×512 or 720×576. Most of these images are available as TIFF files from the University of Southern California's Signal and Image Processing Institute. Kodak has released 768×512 images, available as PNGs, that was originally on Photo CD with higher resolution, that are widely used for comparing image compression techniques.

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  Software intelligence

  Software intelligence is insight into the inner workings and structural condition of software assets produced by software designed to analyze database structure, software framework and source code to better understand and control complex software systems in information technology environments. Similarly to business intelligence (BI), software intelligence is produced by a set of software tools and techniques for the mining of data and the software's inner-structure. Results are automatically produced and feed a knowledge base containing technical documentation and blueprints of the innerworking of applications, and make it available to all to be used by business and software stakeholders to make informed decisions, measure the efficiency of software development organizations, communicate about the software health, prevent software catastrophes. == History == Software intelligence has been used by Kirk Paul Lafler, an American engineer, entrepreneur, and consultant, and founder of Software Intelligence Corporation in 1979. At that time, it was mainly related to SAS activities, in which he has been an expert since 1979. In the early 1980s, Victor R. Basili participated in different papers detailing a methodology for collecting valid software engineering data relating to software engineering, evaluation of software development, and variations. In 2004, different software vendors in software analysis started using the terms as part of their product naming and marketing strategy. Then in 2010, Ahmed E. Hassan and Tao Xie defined software intelligence as a "practice offering software practitioners up-to-date and pertinent information to support their daily decision-making processes and Software Intelligence should support decision-making processes throughout the lifetime of a software system". They go on by defining software intelligence as a "strong impact on modern software practice" for the upcoming decades. == Capabilities == Because of the complexity and wide range of components and subjects implied in software, software intelligence is derived from different aspects of software: Software composition is the construction of software application components. Components result from software coding, as well as the integration of the source code from external components: Open source, 3rd party components, or frameworks. Other components can be integrated using application programming interface call to libraries or services. Software architecture refers to the structure and organization of elements of a system, relations, and properties among them. Software flaws designate problems that can cause security, stability, resiliency, and unexpected results. There is no standard definition of software flaws but the most accepted is from The MITRE Corporation where common flaws are cataloged as Common Weakness Enumeration. Software grades assess attributes of the software. Historically, the classification and terminology of attributes have been derived from the ISO 9126-3 and the subsequent ISO 25000:2005 quality model. Software economics refers to the resource evaluation of software in the past, present, or future to make decisions and to govern. == Components == The capabilities of software intelligence platforms include an increasing number of components: Code analyzer to serve as an information basis for other software intelligence components identifying objects created by the programming language, external objects from Open source, third parties objects, frameworks, API, or services Graphical visualization and blueprinting of the inner structure of the software product or application considered including dependencies, from data acquisition (automated and real-time data capture, end-user entries) up to data storage, the different layers within the software, and the coupling between all elements. Navigation capabilities within components and impact analysis features List of flaws, architectural and coding violations, against standardized best practices, cloud blocker preventing migration to a Cloud environment, and rogue data-call entailing the security and integrity of software Grades or scores of the structural and software quality aligned with industry-standard like OMG, CISQ or SEI assessing the reliability, security, efficiency, maintainability, and scalability to cloud or other systems. Metrics quantifying and estimating software economics including work effort, sizing, and technical debt Industry references and benchmarking allowing comparisons between outputs of analysis and industry standards == User aspect == Some considerations must be made in order to successfully integrate the usage of software Intelligence systems in a company. Ultimately the software intelligence system must be accepted and utilized by the users in order for it to add value to the organization. If the system does not add value to the users' mission, they simply don't use it as stated by M. Storey in 2003. At the code level and system representation, software intelligence systems must provide a different level of abstractions: an abstract view for designing, explaining and documenting and a detailed view for understanding and analyzing the software system. At the governance level, the user acceptance for software intelligence covers different areas related to the inner functioning of the system as well as the output of the system. It encompasses these requirements: Comprehensive: missing information may lead to a wrong or inappropriate decision, as well as it is a factor influencing the user acceptance of a system. Accurate: accuracy depends on how the data is collected to ensure fair and indisputable opinion and judgment. Precise: precision is usually judged by comparing several measurements from the same or different sources. Scalable: lack of scalability in the software industry is a critical factor leading to failure. Credible: outputs must be trusted and believed. Deploy-able and usable. == Applications == Software intelligence has many applications in all businesses relating to the software environment, whether it is software for professionals, individuals, or embedded software. Depending on the association and the usage of the components, applications will relate to: Change and modernization: uniform documentation and blueprinting on all inner components, external code integrated, or call to internal or external components of the software Resiliency and security: measuring against industry standards to diagnose structural flaws in an IT environment. Compliance validation regarding security, specific regulations or technical matters. Decisions making and governance: Providing analytics about the software itself or stakeholders involved in the development of the software, e.g. productivity measurement to inform business and IT leaders about progress towards business goals. Assessment and Benchmarking to help business and IT leaders to make informed, fact-based decision about software. == Marketplace == Software intelligence is a high-level discipline and has been gradually growing covering the applications listed above. There are several markets driving the need for it: Application Portfolio Analysis (APA) aiming at improving the enterprise performance. Software Assessment for producing the software KPI and improving quality and productivity. Software security and resiliency measures and validation. Software evolution or legacy modernization, for which blueprinting the software systems are needed nor tools improving and facilitating modifications.

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  OpenSMILE

  openSMILE is source-available software for automatic extraction of features from audio signals and for classification of speech and music signals. "SMILE" stands for "Speech & Music Interpretation by Large-space Extraction". The software is mainly applied in the area of automatic emotion recognition and is widely used in the affective computing research community. The openSMILE project exists since 2008 and is maintained by the German company audEERING GmbH since 2013. openSMILE is provided free of charge for research purposes and personal use under a source-available license. For commercial use of the tool, the company audEERING offers custom license options. == Application Areas == openSMILE is used for academic research as well as for commercial applications in order to automatically analyze speech and music signals in real-time. In contrast to automatic speech recognition which extracts the spoken content out of a speech signal, openSMILE is capable of recognizing the characteristics of a given speech or music segment. Examples for such characteristics encoded in human speech are a speaker's emotion, age, gender, and personality, as well as speaker states like depression, intoxication, or vocal pathological disorders. The software further includes music classification technology for automatic music mood detection and recognition of chorus segments, key, chords, tempo, meter, dance-style, and genre. The openSMILE toolkit serves as benchmark in manifold research competitions such as Interspeech ComParE, AVEC, MediaEval, and EmotiW. == History == The openSMILE project was started in 2008 by Florian Eyben, Martin Wöllmer, and Björn Schuller at the Technical University of Munich within the European Union research project SEMAINE. The goal of the SEMAINE project was to develop a virtual agent with emotional and social intelligence. In this system, openSMILE was applied for real-time analysis of speech and emotion. The final SEMAINE software release is based on openSMILE version 1.0.1. In 2009, the emotion recognition toolkit (openEAR) was published based on openSMILE. "EAR" stands for "Emotion and Affect Recognition". In 2010, openSMILE version 1.0.1 was published and was introduced and awarded at the ACM Multimedia Open-Source Software Challenge. Between 2011 and 2013, the technology of openSMILE was extended and improved by Florian Eyben and Felix Weninger in the context of their doctoral thesis at the Technical University of Munich. The software was also applied for the project ASC-Inclusion, which was funded by the European Union. For this project, the software was extended by Erik Marchi in order to teach emotional expression to autistic children, based on automatic emotion recognition and visualization. In 2013, the company audEERING acquired the rights to the code-base from the Technical University of Munich and version 2.0 was published under a source-available research license. Until 2016, openSMILE was downloaded more than 50,000 times worldwide and has established itself as a standard toolkit for emotion recognition. == Awards == openSMILE was awarded in 2010 in the context of the ACM Multimedia Open Source Competition. The software tool is applied in numerous scientific publications on automatic emotion recognition. openSMILE and its extension openEAR have been cited in more than 1000 scientific publications until today.

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  Data (word)

  The word data is most often used as a singular collective mass noun in educated everyday usage. However, due to the history and etymology of the word, considerable controversy has existed on whether it should be considered a mass noun used with verbs conjugated in the singular, or should be treated as the plural of the now-rarely-used datum. == Usage in English == In one sense, data is the plural form of datum. Datum actually can also be a count noun with the plural datums (see usage in datum article) that can be used with cardinal numbers (e.g., "80 datums"); data (originally a Latin plural) is not used like a normal count noun with cardinal numbers and can be plural with plural determiners such as these and many, or it can be used as a mass noun with a verb in the singular form. Even when a very small quantity of data is referenced (one number, for example), the phrase piece of data is often used, as opposed to datum. The debate over appropriate usage continues, but "data" as a singular form is far more common. In English, the word datum is still used in the general sense of "an item given". In cartography, geography, nuclear magnetic resonance and technical drawing, it is often used to refer to a single specific reference datum from which distances to all other data are measured. Any measurement or result is a datum, though data point is now far more common. Data is indeed most often used as a singular mass noun in educated everyday usage. Some major newspapers, such as The New York Times, use it either in the singular or plural. In The New York Times, the phrases "the survey data are still being analyzed" and "the first year for which data is available" have appeared within one day. The Wall Street Journal explicitly allows this usage in its style guide. The Associated Press style guide classifies data as a collective noun that takes the singular when treated as a unit but the plural when referring to individual items (e.g., "The data is sound" and "The data have been carefully collected"). In scientific writing, data is often treated as a plural, as in These data do not support the conclusions, but the word is also used as a singular mass entity like information (e.g., in computing and related disciplines). British usage now widely accepts treating data as singular in standard English, including everyday newspaper usage at least in non-scientific use. UK scientific publishing still prefers treating it as a plural. Some UK university style guides recommend using data for both singular and plural use, and others recommend treating it only as a singular in connection with computers. The IEEE Computer Society allows usage of data as either a mass noun or plural based on author preference, while IEEE in the editorial style manual indicates to always use the plural form. Some professional organizations and style guides require that authors treat data as a plural noun. For example, the Air Force Flight Test Center once stated that the word data is always plural, never singular.

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  XLeratorDB

  XLeratorDB is a suite of database function libraries that enable Microsoft SQL Server to perform a wide range of additional (non-native) business intelligence and ad hoc analytics. The libraries, which are embedded and run centrally on the database, include more than 450 individual functions similar to those found in Microsoft Excel spreadsheets. The individual functions are grouped and sold as six separate libraries based on usage: finance, statistics, math, engineering, unit conversions and strings. WestClinTech, the company that developed XLeratorDB, claims it is "the first commercial function package add-in for Microsoft SQL Server." == Company history == WestClinTech (LLC), founded by software industry veterans Charles Flock and Joe Stampf in 2008, is located in Irvington, New York, United States. Flock was a co-founder of The Frustum Group, developer of the OPICS enterprise banking and trading platform, which was acquired by London-based Misys, PLC in 1996. Stampf joined Frustum in 1994 and with Flock remained active with the company after acquisition, helping to develop successive generations of OPICS now employed by over 150 leading financial institutions worldwide. Following a full year of research, development and testing, WestClinTech introduced and recorded its first commercial sale of XLeratorDB in April 2009. In September 2009, XLeratorDB became available to all Federal agencies through NASA's Strategic Enterprise-Wide Procurement (SEWP-IV) program, a government-wide acquisition contract. == Technology == XLeratorDB uses Microsoft SQL CLR(Common Language Runtime) technology. SQL CLR allows managed code to be hosted by, and run in, the Microsoft SQL Server environment. SQL CLR relies on the creation, deployment and registration of .NET Framework assemblies that are physically stored in managed code dynamic-link libraries (DLL). The assemblies may contain .NET namespaces, classes, functions, and properties. Because managed code compiles to native code prior to execution, functions using SQL CLR can achieve significant performance increases versus the equivalent functions written in T-SQL in some scenarios. XLeratorDB requires Microsoft SQL Server 2005 or SQL Server 2005 Express editions, or later (compatibility mode 90 or higher). The product installs with PERMISSION_SET=SAFE. SAFE mode, the most restrictive permission set, is accessible by all users. Code executed by an assembly with SAFE permissions cannot access external system resources such as files, the network, the internet, environment variables, or the registry. == Functions == In computer science, a function is a portion of code within a larger program which performs a specific task and is relatively independent of the remaining code. As used in database and spreadsheet applications these functions generally represent mathematical formulas widely used across a variety of fields. While this code may be user-generated, it is also embedded as a pre-written sub-routine in applications. These functions are typically identified by common nomenclature which corresponds to their underlying operations: e.g. IRR identifies the function which calculates Internal Rate of Return on a series of periodic cash flows. === Function uses === As subroutines, functions can be integrated and used in a variety of ways, and as part of larger, more complicated applications. Within large enterprise applications they may, for example, play an important role in defining business rules or risk management parameters, while remaining virtually invisible to end users. Within database management systems and spreadsheets, however, these kinds of functions also represent discrete sets of tools; they can be accessed directly and utilized on a stand-alone basis, or in more complex, user-defined configurations. In this context, functions can be used for business intelligence and ad hoc analysis of data in fields such as finance, statistics, engineering, math, etc. === Function types === XLeratorDB uses three kinds of functions to perform analytic operations: scalar, aggregate, and a hybrid form which WestClinTech calls Range Queries. Scalar functions take a single value, perform an operation and return a single value. An example of this type of function is LOG, which returns the logarithm of a number to a specified base. Aggregate functions operate on a series of values but return a single, summarizing value. An example of this type of function is AVG, which returns the average of values in a specified group. In XLeratorDB there are some functions which have characteristics of aggregate functions (operating on multiple series of values) but cannot be processed in SQL CLR using single column inputs, such as AVG does. For example, irregular internal rate of return (XIRR), a financial function, operates on a collection of cash flow values from one column, but must also apply variable period lengths from another column and an initial iterative assumption from a third, in order to return a single, summarizing value. WestClinTech documentation notes that Range Queries specify the data to be included in the result set of the function independently of the WHERE clause associated with the T-SQL statement, by incorporating a SELECT statement into the function as a string argument; the function then traps that SELECT statement, executes it internally and processes the result. Some XLeratorDB functions that employ Range Queries are: NPV, XNPV, IRR, XIRR, MIRR, MULTINOMIAL, and SERIESSUM. Within the application these functions are identified by a "_q" naming convention: e.g. NPV_q, IRR_q, etc. == Analytic functions == === SQL Server functions === Microsoft SQL Server is the #3 selling database management system (DBMS), behind Oracle and IBM. (While versions of SQL Server have been on the market since 1987, XLeratorDB is compatible with only the 2005 edition and later.) Like all major DBMS, SQL Server performs a variety of data mining operations by returning or arraying data in different views (also known as drill-down). In addition, SQL Server uses Transact-SQL (T-SQL) to execute four major classes of pre-defined functions in native mode. Functions operating on the DBMS offer several advantages over client layer applications like Excel: they utilize the most up-to-date data available; they can process far larger quantities of data; and, the data is not subject to exporting and transcription errors. SQL Server 2008 includes a total of 58 functions that perform relatively basic aggregation (12), math (23) and string manipulation (23) operations useful for analytics; it includes no native functions that perform more complex operations directly related to finance, statistics or engineering. === Excel functions === Microsoft Excel, a component of Microsoft Office suite, is one of the most widely used spreadsheet applications on the market today. In addition to its inherent utility as a stand-alone desktop application, Excel overlaps and complements the functionality of DBMS in several ways: storing and arraying data in rows and columns; performing certain basic tasks such as pivot table and aggregating values; and facilitating sharing, importing and exporting of database data. Excel's chief limitation relative to a true database is capacity; Excel 2003 is limited to some 65k rows and 256 columns; Excel 2007 extends this capacity to roughly 1million rows and 16k columns. By comparison, SQL Server is able to manage over 500k terabytes of memory. Excel offers, however, an extensive library of specialized pre-written functions which are useful for performing ad hoc analysis on database data. Excel 2007 includes over 300 of these pre-defined functions, although customized functions can also be created by users, or imported from third party developers as add-ons. Excel functions are grouped by type: === Excel business intelligence functions === Operating on the client computing layer Excel plays an important role as a business intelligence tool because it: performs a wide array of complex analytic functions not native to most DBMS software offers far greater ad hoc reporting and analytic flexibility than most enterprise software provides a medium for sharing and collaborating because of its ubiquity throughout the enterprise Microsoft reinforces this positioning with Business Intelligence documentation that positions Excel in a clearly pivotal role. === XLeratorDB vs. Excel functions === While operating within the database environment, XLeratorDB functions utilize the same naming conventions and input formats, and in most cases, return the same calculation results as Excel functions. XLeratorDB, coupled with SQL Server's native capabilities, compares to Excel's function sets as follows:

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  Collision problem

  The r-to-1 collision problem is an important theoretical problem in complexity theory, quantum computing, and computational mathematics. The collision problem most often refers to the 2-to-1 version: given n {\displaystyle n} even and a function f : { 1 , … , n } → { 1 , … , n } {\displaystyle f:\,\{1,\ldots ,n\}\rightarrow \{1,\ldots ,n\}} , we are promised that f is either 1-to-1 or 2-to-1. We are only allowed to make queries about the value of f ( i ) {\displaystyle f(i)} for any i ∈ { 1 , … , n } {\displaystyle i\in \{1,\ldots ,n\}} . The problem then asks how many such queries we need to make to determine with certainty whether f is 1-to-1 or 2-to-1. == Classical solutions == === Deterministic === Solving the 2-to-1 version deterministically requires n 2 + 1 {\textstyle {\frac {n}{2}}+1} queries, and in general distinguishing r-to-1 functions from 1-to-1 functions requires n r + 1 {\textstyle {\frac {n}{r}}+1} queries. This is a straightforward application of the pigeonhole principle: if a function is r-to-1, then after n r + 1 {\textstyle {\frac {n}{r}}+1} queries we are guaranteed to have found a collision. If a function is 1-to-1, then no collision exists. Thus, n r + 1 {\textstyle {\frac {n}{r}}+1} queries suffice. If we are unlucky, then the first n / r {\displaystyle n/r} queries could return distinct answers, so n r + 1 {\textstyle {\frac {n}{r}}+1} queries is also necessary. === Randomized === If we allow randomness, the problem is easier. By the birthday paradox, if we choose (distinct) queries at random, then with high probability we find a collision in any fixed 2-to-1 function after Θ ( n ) {\displaystyle \Theta ({\sqrt {n}})} queries. == Quantum solution == The BHT algorithm, which uses Grover's algorithm, solves this problem optimally by only making O ( n 1 / 3 ) {\displaystyle O(n^{1/3})} queries to f. The matching lower bound of Ω ( n 1 / 3 ) {\displaystyle \Omega (n^{1/3})} was proved by Aaronson and Shi using the polynomial method.

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  Learning augmented algorithm

  A learning augmented algorithm (also called algorithm with predictions) is an algorithm that can make use of a prediction to improve its performance. Whereas in regular algorithms just the problem instance is inputted, learning augmented algorithms accept an extra parameter. This extra parameter often is a prediction of some property of the solution. This prediction is then used by the algorithm to improve its running time or the quality of its output. The most common application are online algorithms, where a prediction on the uncertain instance is provided. == Description == A learning augmented algorithm typically takes an input ( I , A ) {\displaystyle ({\mathcal {I}},{\mathcal {A}})} . Here I {\displaystyle {\mathcal {I}}} is a problem instance and A {\displaystyle {\mathcal {A}}} is the prediction. A prediction can be any object. Common are the following types: Prediction of an optimal solution. The prediction gives a solution to the problem or characterizes an optimal solution. Prediction of the input. This is mainly used for online problems. Prediction of algorithmic actions. A prediction tailored to a specific algorithm that suggests a specific algorithm execution. Learning augmented algorithms usually satisfy the following three properties: Consistency. A learning augmented algorithm is said to be consistent if the algorithm can be proven to have a good performance when it is provided with an accurate prediction. Smoothness. A learning augmented algorithm is called smooth if its performance can be bounded by a function of the quality of the prediction. Here, the quality can be measured in a problem specific way. This is also called the prediction error. Robustness. A learning augmented algorithm is called robust if its worst-case performance can be bounded even if the given prediction is inaccurate. Learning augmented algorithms generally do not prescribe how the prediction should be done. For this purpose machine learning can be used. == Applications == A few examples of problems where learning augmented algorithms have been applied are the following. === Online algorithms === The ski rental problem The weighted paging problem The set cover problem Nonclairvoyant scheduling The online bipartite matching problem === Warm starting === ==== Data structures ==== The binary search algorithm is an algorithm for finding elements of a sorted list x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} . It needs O ( log ⁡ ( n ) ) {\displaystyle O(\log(n))} steps to find an element with some known value y {\displaystyle y} in a list of length n {\displaystyle n} . With a prediction i {\displaystyle i} for the position of y {\displaystyle y} , the following learning augmented algorithm can be used. First, look at position i {\displaystyle i} in the list. If x i = y {\displaystyle x_{i}=y} , the element has been found. If x i < y {\displaystyle x_{i} y {\displaystyle x_{i}>y} , do the same as in the previous case, but instead consider i − 1 , i − 2 , i − 4 , … {\displaystyle i-1,i-2,i-4,\ldots } . The error is defined to be η = | i − i ∗ | {\displaystyle \eta =|i-i^{}|} , where i ∗ {\displaystyle i^{}} is the real index of y {\displaystyle y} . In the learning augmented algorithm, probing the positions i + 1 , i + 2 , i + 4 , … {\displaystyle i+1,i+2,i+4,\ldots } takes log 2 ⁡ ( η ) {\displaystyle \log _{2}(\eta )} steps. Then a binary search is performed on a list of size at most 2 η {\displaystyle 2\eta } , which takes log 2 ⁡ ( η ) {\displaystyle \log _{2}(\eta )} steps. This makes the total running time of the algorithm 2 log 2 ⁡ ( η ) {\displaystyle 2\log _{2}(\eta )} . So, when the error is small, the algorithm is faster than a normal binary search. This shows that the algorithm is consistent. Even in the worst case, the error will be at most n {\displaystyle n} . Then the algorithm takes at most O ( log ⁡ ( n ) ) {\displaystyle O(\log(n))} steps, so the algorithm is robust. ==== More examples ==== The maximum weight matching problem === Approximation algorithms === The maximum cut problem The vertex cover problem === Mechanism Design === The facility location problem

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  Generalized distributive law

  The generalized distributive law (GDL) is a generalization of the distributive property which gives rise to a general message passing algorithm. It is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence communities. The law and algorithm were introduced in a semi-tutorial by Srinivas M. Aji and Robert J. McEliece with the same title. == Introduction == "The distributive law in mathematics is the law relating the operations of multiplication and addition, stated symbolically, a ∗ ( b + c ) = a ∗ b + a ∗ c {\displaystyle a(b+c)=ab+ac} ; that is, the monomial factor a {\displaystyle a} is distributed, or separately applied, to each term of the binomial factor b + c {\displaystyle b+c} , resulting in the product a ∗ b + a ∗ c {\displaystyle ab+ac} " – Britannica. As it can be observed from the definition, application of distributive law to an arithmetic expression reduces the number of operations in it. In the previous example the total number of operations reduced from three (two multiplications and an addition in a ∗ b + a ∗ c {\displaystyle ab+ac} ) to two (one multiplication and one addition in a ∗ ( b + c ) {\displaystyle a(b+c)} ). Generalization of distributive law leads to a large family of fast algorithms. This includes the FFT and Viterbi algorithm. This is explained in a more formal way in the example below: α ( a , b ) = d e f ∑ c , d , e ∈ A f ( a , c , b ) g ( a , d , e ) {\displaystyle \alpha (a,\,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c,d,e\in A}f(a,\,c,\,b)\,g(a,\,d,\,e)} where f ( ⋅ ) {\displaystyle f(\cdot )} and g ( ⋅ ) {\displaystyle g(\cdot )} are real-valued functions, a , b , c , d , e ∈ A {\displaystyle a,b,c,d,e\in A} and | A | = q {\displaystyle |A|=q} (say) Here we are "marginalizing out" the independent variables ( c {\displaystyle c} , d {\displaystyle d} , and e {\displaystyle e} ) to obtain the result. When we are calculating the computational complexity, we can see that for each q 2 {\displaystyle q^{2}} pairs of ( a , b ) {\displaystyle (a,b)} , there are q 3 {\displaystyle q^{3}} terms due to the triplet ( c , d , e ) {\displaystyle (c,d,e)} which needs to take part in the evaluation of α ( a , b ) {\displaystyle \alpha (a,\,b)} with each step having one addition and one multiplication. Therefore, the total number of computations needed is 2 ⋅ q 2 ⋅ q 3 = 2 q 5 {\displaystyle 2\cdot q^{2}\cdot q^{3}=2q^{5}} . Hence the asymptotic complexity of the above function is O ( n 5 ) {\displaystyle O(n^{5})} . If we apply the distributive law to the RHS of the equation, we get the following: α ( a , b ) = d e f ∑ c ∈ A f ( a , c , b ) ⋅ ∑ d , e ∈ A g ( a , d , e ) {\displaystyle \alpha (a,\,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c\in A}f(a,\,c,\,b)\cdot \sum _{d,\,e\in A}g(a,\,d,\,e)} This implies that α ( a , b ) {\displaystyle \alpha (a,\,b)} can be described as a product α 1 ( a , b ) ⋅ α 2 ( a ) {\displaystyle \alpha _{1}(a,\,b)\cdot \alpha _{2}(a)} where α 1 ( a , b ) = d e f ∑ c ∈ A f ( a , c , b ) {\displaystyle \alpha _{1}(a,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c\in A}f(a,\,c,\,b)} and α 2 ( a ) = d e f ∑ d , e ∈ A g ( a , d , e ) {\displaystyle \alpha _{2}(a){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{d,\,e\in A}g(a,\,d,\,e)} Now, when we are calculating the computational complexity, we can see that there are q 3 {\displaystyle q^{3}} additions in α 1 ( a , b ) {\displaystyle \alpha _{1}(a,\,b)} and α 2 ( a ) {\displaystyle \alpha _{2}(a)} each and there are q 2 {\displaystyle q^{2}} multiplications when we are using the product α 1 ( a , b ) ⋅ α 2 ( a ) {\displaystyle \alpha _{1}(a,\,b)\cdot \alpha _{2}(a)} to evaluate α ( a , b ) {\displaystyle \alpha (a,\,b)} . Therefore, the total number of computations needed is q 3 + q 3 + q 2 = 2 q 3 + q 2 {\displaystyle q^{3}+q^{3}+q^{2}=2q^{3}+q^{2}} . Hence the asymptotic complexity of calculating α ( a , b ) {\displaystyle \alpha (a,b)} reduces to O ( n 3 ) {\displaystyle O(n^{3})} from O ( n 5 ) {\displaystyle O(n^{5})} . This shows by an example that applying distributive law reduces the computational complexity which is one of the good features of a "fast algorithm". == History == Some of the problems that used distributive law to solve can be grouped as follows: Decoding algorithms: A GDL like algorithm was used by Gallager's for decoding low density parity-check codes. Based on Gallager's work Tanner introduced the Tanner graph and expressed Gallagers work in message passing form. The tanners graph also helped explain the Viterbi algorithm. It is observed by Forney that Viterbi's maximum likelihood decoding of convolutional codes also used algorithms of GDL-like generality. Forward–backward algorithm: The forward backward algorithm helped as an algorithm for tracking the states in the Markov chain. And this also was used the algorithm of GDL like generality Artificial intelligence: The notion of junction trees has been used to solve many problems in AI. Also the concept of bucket elimination used many of the concepts. == The MPF problem == MPF or marginalize a product function is a general computational problem which as special case includes many classical problems such as computation of discrete Hadamard transform, maximum likelihood decoding of a linear code over a memory-less channel, and matrix chain multiplication. The power of the GDL lies in the fact that it applies to situations in which additions and multiplications are generalized. A commutative semiring is a good framework for explaining this behavior. It is defined over a set K {\displaystyle K} with operators " + {\displaystyle +} " and " . {\displaystyle .} " where ( K , + ) {\displaystyle (K,\,+)} and ( K , . ) {\displaystyle (K,\,.)} are a commutative monoids and the distributive law holds. Let p 1 , … , p n {\displaystyle p_{1},\ldots ,p_{n}} be variables such that p 1 ∈ A 1 , … , p n ∈ A n {\displaystyle p_{1}\in A_{1},\ldots ,p_{n}\in A_{n}} where A {\displaystyle A} is a finite set and | A i | = q i {\displaystyle |A_{i}|=q_{i}} . Here i = 1 , … , n {\displaystyle i=1,\ldots ,n} . If S = { i 1 , … , i r } {\displaystyle S=\{i_{1},\ldots ,i_{r}\}} and S ⊂ { 1 , … , n } {\displaystyle S\,\subset \{1,\ldots ,n\}} , let A S = A i 1 × ⋯ × A i r {\displaystyle A_{S}=A_{i_{1}}\times \cdots \times A_{i_{r}}} , p S = ( p i 1 , … , p i r ) {\displaystyle p_{S}=(p_{i_{1}},\ldots ,p_{i_{r}})} , q S = | A S | {\displaystyle q_{S}=|A_{S}|} , A = A 1 × ⋯ × A n {\displaystyle \mathbf {A} =A_{1}\times \cdots \times A_{n}} , and p = { p 1 , … , p n } {\displaystyle \mathbf {p} =\{p_{1},\ldots ,p_{n}\}} Let S = { S j } j = 1 M {\displaystyle S=\{S_{j}\}_{j=1}^{M}} where S j ⊂ { 1 , . . . , n } {\displaystyle S_{j}\subset \{1,...\,,n\}} . Suppose a function is defined as α i : A S i → R {\displaystyle \alpha _{i}:A_{S_{i}}\rightarrow R} , where R {\displaystyle R} is a commutative semiring. Also, p S i {\displaystyle p_{S_{i}}} are named the local domains and α i {\displaystyle \alpha _{i}} as the local kernels. Now the global kernel β : A → R {\displaystyle \beta :\mathbf {A} \rightarrow R} is defined as: β ( p 1 , . . . , p n ) = ∏ i = 1 M α ( p S i ) {\displaystyle \beta (p_{1},...\,,p_{n})=\prod _{i=1}^{M}\alpha (p_{S_{i}})} Definition of MPF problem: For one or more indices i = 1 , . . . , M {\displaystyle i=1,...\,,M} , compute a table of the values of S i {\displaystyle S_{i}} -marginalization of the global kernel β {\displaystyle \beta } , which is the function β i : A S i → R {\displaystyle \beta _{i}:A_{S_{i}}\rightarrow R} defined as β i ( p S i ) = ∑ p S i c ∈ A S i c β ( p ) {\displaystyle \beta _{i}(p_{S_{i}})\,=\displaystyle \sum \limits _{p_{S_{i}^{c}}\in A_{S_{i}^{c}}}\beta (p)} Here S i c {\displaystyle S_{i}^{c}} is the complement of S i {\displaystyle S_{i}} with respect to { 1 , . . . , n } {\displaystyle \mathbf {\{} 1,...\,,n\}} and the β i ( p S i ) {\displaystyle \beta _{i}(p_{S_{i}})} is called the i t h {\displaystyle i^{th}} objective function, or the objective function at S i {\displaystyle S_{i}} . It can observed that the computation of the i t h {\displaystyle i^{th}} objective function in the obvious way needs M q 1 q 2 q 3 ⋯ q n {\displaystyle Mq_{1}q_{2}q_{3}\cdots q_{n}} operations. This is because there are q 1 q 2 ⋯ q n {\displaystyle q_{1}q_{2}\cdots q_{n}} additions and ( M − 1 ) q 1 q 2 . . . q n {\displaystyle (M-1)q_{1}q_{2}...q_{n}} multiplications needed in the computation of the i th {\displaystyle i^{\text{th}}} objective function. The GDL algorithm which is explained in the next section can reduce this computational complexity. The following is an example of the MPF problem. Let p 1 , p 2 , p 3 , p 4 , {\displaystyle p_{1},\,p_{2},\,p_{3},\,p_{4},} and p 5 {\displaystyle p_{5}} be variables such that p 1 ∈ A 1 , p 2 ∈ A 2 , p 3 ∈ A 3 , p 4 ∈ A 4 , {\displaystyle p_{1}\in

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  Granular computing

  Granular computing is an emerging computing paradigm of information processing that concerns the processing of complex information entities called "information granules", which arise in the process of data abstraction and derivation of knowledge from information or data. Generally speaking, information granules are collections of entities that usually originate at the numeric level and are arranged together due to their similarity, functional or physical adjacency, indistinguishability, coherency, or the like. At present, granular computing is more a theoretical perspective than a coherent set of methods or principles. As a theoretical perspective, it encourages an approach to data that recognizes and exploits the knowledge present in data at various levels of resolution or scales. In this sense, it encompasses all methods which provide flexibility and adaptability in the resolution at which knowledge or information is extracted and represented. == Types of granulation == As mentioned above, granular computing is not an algorithm or process; there is no particular method that is called "granular computing". It is rather an approach to looking at data that recognizes how different and interesting regularities in the data can appear at different levels of granularity, much as different features become salient in satellite images of greater or lesser resolution. On a low-resolution satellite image, for example, one might notice interesting cloud patterns representing cyclones or other large-scale weather phenomena, while in a higher-resolution image, one misses these large-scale atmospheric phenomena but instead notices smaller-scale phenomena, such as the interesting pattern that is the streets of Manhattan. The same is generally true of all data: At different resolutions or granularities, different features and relationships emerge. The aim of granular computing is to try to take advantage of this fact in designing more effective machine-learning and reasoning systems. There are several types of granularity that are often encountered in data mining and machine learning, and we review them below: === Value granulation (discretization/quantization) === One type of granulation is the quantization of variables. It is very common that in data mining or machine-learning applications the resolution of variables needs to be decreased in order to extract meaningful regularities. An example of this would be a variable such as "outside temperature" (temp), which in a given application might be recorded to several decimal places of precision (depending on the sensing apparatus). However, for purposes of extracting relationships between "outside temperature" and, say, "number of health-club applications" (club), it will generally be advantageous to quantize "outside temperature" into a smaller number of intervals. ==== Motivations ==== There are several interrelated reasons for granulating variables in this fashion: Based on prior domain knowledge, there is no expectation that minute variations in temperature (e.g., the difference between 80–80.7 °F (26.7–27.1 °C)) could have an influence on behaviors driving the number of health-club applications. For this reason, any "regularity" which our learning algorithms might detect at this level of resolution would have to be spurious, as an artifact of overfitting. By coarsening the temperature variable into intervals the difference between which we do anticipate (based on prior domain knowledge) might influence number of health-club applications, we eliminate the possibility of detecting these spurious patterns. Thus, in this case, reducing resolution is a method of controlling overfitting. By reducing the number of intervals in the temperature variable (i.e., increasing its grain size), we increase the amount of sample data indexed by each interval designation. Thus, by coarsening the variable, we increase sample sizes and achieve better statistical estimation. In this sense, increasing granularity provides an antidote to the so-called curse of dimensionality, which relates to the exponential decrease in statistical power with increase in number of dimensions or variable cardinality. Independent of prior domain knowledge, it is often the case that meaningful regularities (i.e., which can be detected by a given learning methodology, representational language, etc.) may exist at one level of resolution and not at another. For example, a simple learner or pattern recognition system may seek to extract regularities satisfying a conditional probability threshold such as p ( Y = y j | X = x i ) ≥ α . {\displaystyle p(Y=y_{j}|X=x_{i})\geq \alpha .} In the special case where α = 1 , {\displaystyle \alpha =1,} this recognition system is essentially detecting logical implication of the form X = x i → Y = y j {\displaystyle X=x_{i}\rightarrow Y=y_{j}} or, in words, "if X = x i , {\displaystyle X=x_{i},} then Y = y j {\displaystyle Y=y_{j}} ". The system's ability to recognize such implications (or, in general, conditional probabilities exceeding threshold) is partially contingent on the resolution with which the system analyzes the variables. As an example of this last point, consider the feature space shown to the right. The variables may each be regarded at two different resolutions. Variable X {\displaystyle X} may be regarded at a high (quaternary) resolution wherein it takes on the four values { x 1 , x 2 , x 3 , x 4 } {\displaystyle \{x_{1},x_{2},x_{3},x_{4}\}} or at a lower (binary) resolution wherein it takes on the two values { X 1 , X 2 } . {\displaystyle \{X_{1},X_{2}\}.} Similarly, variable Y {\displaystyle Y} may be regarded at a high (quaternary) resolution or at a lower (binary) resolution, where it takes on the values { y 1 , y 2 , y 3 , y 4 } {\displaystyle \{y_{1},y_{2},y_{3},y_{4}\}} or { Y 1 , Y 2 } , {\displaystyle \{Y_{1},Y_{2}\},} respectively. At the high resolution, there are no detectable implications of the form X = x i → Y = y j , {\displaystyle X=x_{i}\rightarrow Y=y_{j},} since every x i {\displaystyle x_{i}} is associated with more than one y j , {\displaystyle y_{j},} and thus, for all x i , {\displaystyle x_{i},} p ( Y = y j | X = x i ) < 1. {\displaystyle p(Y=y_{j}|X=x_{i})<1.} However, at the low (binary) variable resolution, two bilateral implications become detectable: X = X 1 ↔ Y = Y 1 {\displaystyle X=X_{1}\leftrightarrow Y=Y_{1}} and X = X 2 ↔ Y = Y 2 {\displaystyle X=X_{2}\leftrightarrow Y=Y_{2}} , since every X 1 {\displaystyle X_{1}} occurs iff Y 1 {\displaystyle Y_{1}} and X 2 {\displaystyle X_{2}} occurs iff Y 2 . {\displaystyle Y_{2}.} Thus, a pattern recognition system scanning for implications of this kind would find them at the binary variable resolution, but would fail to find them at the higher quaternary variable resolution. ==== Issues and methods ==== It is not feasible to exhaustively test all possible discretization resolutions on all variables in order to see which combination of resolutions yields interesting or significant results. Instead, the feature space must be preprocessed (often by an entropy analysis of some kind) so that some guidance can be given as to how the discretization process should proceed. Moreover, one cannot generally achieve good results by naively analyzing and discretizing each variable independently, since this may obliterate the very interactions that we had hoped to discover. A sample of papers that address the problem of variable discretization in general, and multiple-variable discretization in particular, is as follows: Chiu, Wong & Cheung (1991), Bay (2001), Liu et al. (2002), Wang & Liu (1998), Zighed, Rabaséda & Rakotomalala (1998), Catlett (1991), Dougherty, Kohavi & Sahami (1995), Monti & Cooper (1999), Fayyad & Irani (1993), Chiu, Cheung & Wong (1990), Nguyen & Nguyen (1998), Grzymala-Busse & Stefanowski (2001), Ting (1994), Ludl & Widmer (2000), Pfahringer (1995), An & Cercone (1999), Chiu & Cheung (1989), Chmielewski & Grzymala-Busse (1996), Lee & Shin (1994), Liu & Wellman (2002), Liu & Wellman (2004). === Variable granulation (clustering/aggregation/transformation) === Variable granulation is a term that could describe a variety of techniques, most of which are aimed at reducing dimensionality, redundancy, and storage requirements. We briefly describe some of the ideas here, and present pointers to the literature. ==== Variable transformation ==== A number of classical methods, such as principal component analysis, multidimensional scaling, factor analysis, and structural equation modeling, and their relatives, fall under the genus of "variable transformation." Also in this category are more modern areas of study such as dimensionality reduction, projection pursuit, and independent component analysis. The common goal of these methods in general is to find a representation of the data in terms of new variables, which are a linear or nonlinear transformation of the original variables, and in which important stati

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  WCF Data Services

  WCF Data Services (formerly ADO.NET Data Services, codename "Astoria") is a platform for what Microsoft calls Data Services. It is actually a combination of the runtime and a web service through which the services are exposed. It also includes the Data Services Toolkit which lets Astoria Data Services be created from within ASP.NET itself. The Astoria project was announced at MIX 2007, and the first developer preview was made available on April 30, 2007. The first CTP was made available as a part of the ASP.NET 3.5 Extensions Preview. The final version was released as part of Service Pack 1 of the .NET Framework 3.5 on August 11, 2008. The name change from ADO.NET Data Services to WCF data Services was announced at the 2009 PDC. == Overview == WCF Data Services exposes data, represented as Entity Data Model (EDM) objects, via web services accessed over HTTP. The data can be addressed using a REST-like URI. The data service, when accessed via the HTTP GET method with such a URI, will return the data. The web service can be configured to return the data in either plain XML, JSON or RDF+XML. In the initial release, formats like RSS and ATOM are not supported, though they may be in the future. In addition, using other HTTP methods like PUT, POST or DELETE, the data can be updated as well. POST can be used to create new entities, PUT for updating an entity, and DELETE for deleting an entity. == Description == Windows Communication Foundation (WCF) comes to the rescue when we find ourselves not able to achieve what we want to achieve using web services, i.e., other protocols support and even duplex communication. With WCF, we can define our service once and then configure it in such a way that it can be used via HTTP, TCP, IPC, and even Message Queues. We can consume Web Services using server side scripts (ASP.NET), JavaScript Object Notations (JSON), and even REST (Representational State Transfer). Understanding the basics When we say that a WCF service can be used to communicate using different protocols and from different kinds of applications, we will need to understand how we can achieve this. If we want to use a WCF service from an application, then we have three major questions: 1.Where is the WCF service located from a client's perspective? 2.How can a client access the service, i.e., protocols and message formats? 3.What is the functionality that a service is providing to the clients? Once we have the answer to these three questions, then creating and consuming the WCF service will be a lot easier for us. The WCF service has the concept of endpoints. A WCF service provides endpoints which client applications can use to communicate with the WCF service. The answer to these above questions is what is known as the ABC of WCF services and in fact are the main components of a WCF service. So let's tackle each question one by one. Address: Like a webservice, a WCF service also provides a URI which can be used by clients to get to the WCF service. This URI is called as the Address of the WCF service. This will solve the first problem of "where to locate the WCF service?" for us. Binding: Once we are able to locate the WCF service, one should think about how to communicate with the service (protocol wise). The binding is what defines how the WCF service handles the communication. It could also define other communication parameters like message encoding, etc. This will solve the second problem of "how to communicate with the WCF service?" for us. Contract: Now the only question one is left with is about the functionalities that a WCF service provides. The contract is what defines the public data and interfaces that WCF service provides to the clients. The URIs representing the data will contain the physical location of the service, as well as the service name. It will also need to specify an EDM Entity-Set or a specific entity instance, as in respectively http://dataserver/service.svc/MusicCollection or http://dataserver/service.svc/MusicCollection[SomeArtist] The former will list all entities in the Collection set whereas the latter will list only for the entity which is indexed by SomeArtist. The URIs can also specify a traversal of a relationship in the Entity Data Model. For example, http://dataserver/service.svc/MusicCollection[SomeSong]/Genre traverses the relationship Genre (in SQL parlance, joins with the Genre table) and retrieves all instances of Genre that are associated with the entity SomeSong. Simple predicates can also be specified in the URI, like http://dataserver/service.svc/MusicCollection[SomeArtist]/ReleaseDate[Year eq 2006] will fetch the items that are indexed by SomeArtist and had their release in 2006. Filtering and partition information can also be encoded in the URL as http://dataserver/service.svc/MusicCollection?$orderby=ReleaseDate&$skip=100&$top=50 Although the presence of skip and top keywords indicates paging support, in Data Services version 1 there is no method of determining the number of records available and thus impossible to determine how many pages there may be. The OData 2.0 spec adds support for the $count path segment (to return just a count of entities) and $inlineCount (to retrieve a page worth of entities and a total count without a separate round-trip....).

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  Lion algorithm

  Lion algorithm (LA) is one among the bio-inspired (or) nature-inspired optimization algorithms (or) that are mainly based on meta-heuristic principles. It was first introduced by B. R. Rajakumar in 2012 in the name, Lion’s Algorithm. It was further extended in 2014 to solve the system identification problem. This version was referred as LA, which has been applied by many researchers for their optimization problems. == Inspiration from lion’s social behaviour == Lions form a social system called a "pride", which consists of 1–3 pair of lions. A pride of lions shares a common area known as territory in which a dominant lion is called as territorial lion. The territorial lion safeguards its territory from outside attackers, especially nomadic lions. This process is called territorial defense. It protects the cubs till they become sexually matured. The maturity period is about 2–4 years. The pride undergoes survival fights to protect its territory and the cubs from nomadic lions. Upon getting defeated by the nomadic lions, the dominating nomadic lion takes the role of territorial lion by killing or driving out the cubs of the pride. The lioness of the pride give birth to cubs though the new territorial lion. When the cubs of the pride mature and considered to be stronger than the territorial lion, they take over the pride. This process is called territorial take-over. If territorial take-over happens, either the old territorial lion, which is considered to be laggard, is driven out or it leaves the pride. The stronger lions and lioness form the new pride and give birth to their own cubs == Terminology == In the LA, the terms that are associated with lion’s social system are mapped to the terminology of optimization problems. Few of such notable terms are related here. Lion: A potential solution to be generated or determined as optimal (or) near-optimal solution of the problem. The lion can be a territorial lion and lioness, cubs and nomadic lions that represent the solution based on the processing steps of the LA. Territorial lion: The strongest solution of the pride that tends to meet the objective function. Nomadic lion: A random solution, sometimes termed as nomad, to facilitate the exploration principle Laggard lion: Poor solutions that are failed in the survival fight. Pride: A pool of potential solutions i.e. a lion, lioness and their cubs, that are potential solutions of the search problem. Fertility evaluation: A process of evaluating whether the territorial lion and lioness are able to provide potential solutions in the future generations i.e. It ensures that the lion or lioness converge at every generation. Survival fight: It is a greedy selection process, which is often carried out between the pride and nomadic lion. == Algorithm == The steps involved in LA are given below: Pride Generation: Generate X m a l e {\displaystyle X^{male}} , X f e m a l e {\displaystyle X^{female}} and X 1 n o m a d {\displaystyle X_{1}^{nomad}} Determine f ( X m a l e ) {\displaystyle f(X^{male})} , f ( X f e m a l e ) {\displaystyle f(X^{female})} , f ( X 1 n o m a d ) {\displaystyle f(X_{1}^{nomad})} Initialize f r e f {\displaystyle f^{ref}} as f ( X m a l e ) {\displaystyle f(X^{male})} and N g {\displaystyle N_{g}} as 0 Memorize X m a l e {\displaystyle X^{male}} and X f e m a l e {\displaystyle X^{female}} Apply Fertility evaluation Process Generation of cubpool by mating Gender clustering: Define X c u b m a l e {\displaystyle X_{cub}^{male}} and X c u b f e m a l e {\displaystyle X_{cub}^{female}} Initialize a g e c u b {\displaystyle age_{cub}} as zero Apply Cub growth function Territorial defense: If X m a l e {\displaystyle X^{male}} (or pride) fails in the survival fight i.e. X 1 n o m a d {\displaystyle X_{1}^{nomad}} defeats the pride, go to step 4, else continue Increase a g e c u b {\displaystyle age_{cub}} by 1 and check whether cub attains maturity i.e., if a g e c u b > a g e m a x {\displaystyle age_{cub}>age_{max}} , go to Step 9, else continue Territorial takeover: If X c u b m a l e {\displaystyle X_{cub}^{male}} and X c u b f e m a l e {\displaystyle X_{cub}^{female}} are found to be closer to optimal solution, update X m a l e {\displaystyle X^{male}} and X f e m a l e {\displaystyle X^{female}} Increment N g {\displaystyle N_{g}} by 1 Repeat from Step 5, if termination criterion is not violated, else return X m a l e {\displaystyle X^{male}} as the near-optimal solution == Variants == The LA has been further taken forward to adopt in different problem areas. According to the characteristics of the problem area, significant amendment has been done in the processes and the models used in the LA. Accordingly, diverse variants have been developed by the researchers. They can be broadly grouped as hybrid LAs and non-hybrid LAs. Hybrid LAs are the LAs that are amended by the principle of other meta-heuristics, whereas the Non-hybrid LAs take any scientific amendment inside its operation that are felt to be essential to attend the respective problem area. == Applications == LA is applied in diverse engineering applications that range from network security, text mining, image processing, electrical systems, data mining and many more. Few of the notable applications are discussed here. Networking applications: In WSN, LA is used to solve the cluster head selection problem by determining optimal cluster head. Route discovery problem in both the VANET and MANET are also addressed by the LA in the literature. It is also used to detect attacks in advanced networking scenarios such as Software-Defined Networks (SDN) Power Systems: LA has attended generation rescheduling problem in a deregulated environment, optimal localization and sizing of FACTS devices for power quality enhancement and load-frequency controlling problem Cloud computing: LA is used in optimal container-resource allocation problem in cloud environment and cloud security

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